Symbols · Operators and calculus
∏ Product (pi notation)
Say it: “the product from i equals 1 to n of”, “product over i”
What it means
A capital pi means: multiply the expression after it for every value of the index, the way ∑ adds. It is common for the likelihood of independent observations.
Read aloud in real formulas
∏ᵢ₌₁ⁿ i = n!
Aethel says
the product from i equals 1 to n of i equals n factorial
multiplying 1 to n gives n factorial
L(θ) = ∏ᵢ p(xᵢ | θ)
Aethel says
L of theta equals the product over i of p of x sub i given theta
the likelihood of independent data
Typing it
- LaTeX
- \prod_{i=1}^{n}
- Unicode
- U+220F
Questions
How do you say ∏ out loud?
It is usually read “the product from i equals 1 to n of”, and also “product over i”.
What does ∏ mean in maths?
A capital pi means: multiply the expression after it for every value of the index, the way ∑ adds. It is common for the likelihood of independent observations.
How do you type ∏?
In LaTeX, write \prod_{i=1}^{n}. Its Unicode code point is U+220F.